Physics 311: Mechanics

Overview

This course is an intermediate undergraduate level course in classical mechanics. The major topics for Physics 311 include the origin and development of classical mechanics; mathematical techniques, especially vector analysis; conservation laws and their relation to symmetry principles; brief introduction to orbit theory and rigid-body dynamics; accelerated coordinate systems; introduction to the generalized-coordinate formalisms of Lagrange and Hamilton; and an introduction to the theory of chaos and nonlinear dynamics. The main goal of the class is to introduce the students to the language and mathematical techniques used for solving problems of mechanics; it also prepares the students for advanced coursework in the physics sequence including electromagnetic fields and statistical physics, and provides the foundation for quantum mechanics by introducing Hamiltonian mechanics. This class also provides the necessary background for advanced topical classes such as plasma physics and fluid mechanics. This course uses differential equations and linear algebra heavily, and relies upon vector calculus for solving problems. Knowledge of multivariate calculus at the level of Math 234 or 375 is required at the outset; it is useful to have taken or be concurrently taking Math 320!, or Math 319 and 340. Math 321 is also helpful. Traditionally, the course is taught with three lectures per week and a weekly problem session.

Topics Covered

This class is intended to give students an introduction to the concepts and mathematics used to describe electromagnetic phenomena. Physics topics usually covered include:
• Origin and development of classical mechanics
• conservation laws and their relation to symmetry principles;
• basic orbit theory including planets and scattering
• rigid-body dynamics
• accelerated coordinate systems
• introduction to the generalized-coordinates
• Introduction to Lagrangian and Hamilton mechanics
• chaos and nonlinear dynamics
• In addition, the class introduces and uses the following mathematics:
• Vector analysis, coordinate transformations
• basic vector calculus, div, the Laplacian, Stoke's.
• Numerical solutions of coupled first order differential equations (Runge-Kutta integration)
• Linear algebra
• Prerequisites

Physics 202, 208, or 248, and Math 234 or 375; or graduate/professional standing.

Standard Texts

Classical Dynamics (fourth edition), J. B. Marion and S.T. Thornton, Saunders College Publishing 1995. Classical Mechanics: A Modern Perspective, 2nd Edition, by Vernon Barger and Martin Olsson (McGraw-Hill, Inc., New York, 1995) ISBN 0-07-003734-5 Mechanics, K. Symon, Addison Wesley (1971). Mechanics, Course of Theoretical Physics Volume 1, L.D. Landau and E.M. Lifshitz, Permagon Press (1976). The Feynman Lectures on Physics [as Reference], R.P. Feynman, R.B. Leighton and M. Sands, Addison-Wesley (1964).
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